def pal

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64int.bend:317

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/generic.bend as SG
import bend-collections-laws-math@1.0.0.0/src/math/generic.bend as G
import bend-collections-laws-math@1.0.0.0/src/math/num.bend as NM
import bend-collections-laws-math@1.0.0.0/src/math/instances.bend as I
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64laws.bend as LW
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU

317def pal(+xs: List<&2, WU.U64>, +r: Maybe<&2, WU.U64>, +n: Nat, +c: Bool, +hr: {r == G.fits(WU.U64, Bool.not(c), of(n)) : Maybe<&2, WU.U64>}, +hc: {C.fits(64n, n) == c : Bool}) -> {G.ok(WU.U64, G.prod_go(~WU.U64, ~I.u64_op, ~I.u64_is, xs, r)) == SG.prefix_fin(~WU.U64, ~SG.u64_of, SG.prod_go(64n, vals(xs), n, c)) : Result<&2, &2, NM.NumError, WU.U64>}:
318  match xs c:
319    case Nil{} True{}:
320      %Equal.sym(Maybe<&2, WU.U64>, r, Some{of(n)}, hr) : {G.ok(WU.U64, _) == Done{of(n)} : Result<&2, &2, NM.NumError, WU.U64>}
321      {==}
322    case Nil{} False{}:
323      %Equal.sym(Maybe<&2, WU.U64>, r, None{}, hr) : {G.ok(WU.U64, _) == Fail{NM.Overflow{}} : Result<&2, &2, NM.NumError, WU.U64>}
324      {==}
325    case Con{x, t} False{}:
326      %Equal.sym(Maybe<&2, WU.U64>, r, None{}, hr) : {G.ok(WU.U64, G.prod_go(~WU.U64, ~I.u64_op, ~I.u64_is, Con{x, t}, _)) == Fail{NM.Overflow{}} : Result<&2, &2, NM.NumError, WU.U64>}
327      {==}
328    case Con{+x, +t} True{}:
329      %Equal.sym(Maybe<&2, WU.U64>, r, Some{of(n)}, hr) : {G.ok(WU.U64, G.prod_go(~WU.U64, ~I.u64_op, ~I.u64_is, Con{x, t}, _)) == SG.prefix_fin(~WU.U64, ~SG.u64_of, SG.prod_go(64n, vals(t), Nat.mul(n, v(x)), C.fits(64n, Nat.mul(n, v(x))))) : Result<&2, &2, NM.NumError, WU.U64>}
330      +hn = Equal.cong(Nat, Nat, z => Nat.mul(z, v(x)), v(of(n)), n, LW.vo(n, hc))
331      pal(t, G.cmul(~WU.U64, ~I.u64_op, ~I.u64_is, of(n), x), Nat.mul(n, v(x)), C.fits(64n, Nat.mul(n, v(x))), cmul_rel(of(n), x, Nat.mul(n, v(x)), hn, C.fits(64n, Nat.mul(n, v(x))), {==}), {==})